Methods and apparatus for ultrawide entrance angle reflective articles for use with autonomous vehicle machine vision systems

ABSTRACT

A two-layer retroreflective article construction is enabled that produces higher wide-entrance-angle performance for signs and pavement markings. A single-layer overlay is enabled for existing signs and pavement markers that improve their entrance angle performance. Materials used in the construction of an article or an overlay are transparent to radiation in the range of 400 to 1000 nanometers and utilize TIR (total internal reflection). Minimum performance specifications are proposed that extend sign sheeting retroreflectivity specifications to entrance angles of 60 degrees. An innovative traffic sign design is enabled that increases the positioning performance of safety systems and automated navigation systems.

PRIORITY

This application claims priority to U.S. Provisional Applications Nos.62/718,183 and 62/753,207, the contents of which are hereby incorporatedby reference.

FIELD OF THE INVENTION

The present disclosure relates generally to optical elements that arereflective, such as reflective road markers. More particularly, thepresent disclosure relates to sign sheeting and pavement markingmaterials that produce higher levels of net retroreflectivity at largerentrance angles and over a broader electromagnetic spectrum.

BACKGROUND OF THE INVENTION

Retroreflective sheeting is often used in roadway signs and conspicuitygarments to increase nighttime visibility. Retroreflective adhesivematerials are used as pavement markers and vehicle reflectors. Suchretroreflective sheeting and materials typically comprise a layer oftransparent material having a substantially smooth front surface, and arear surface provided with a plurality of retroreflective elements. Themost common retroreflective elements are beads or similar sphericalelements having a different index of refraction than the transparentmaterial, or retroreflective geometric features, such as a series oftrihedral-shaped features referred to as cube corners because of theinternal corner that is formed by the three mutually perpendicular flatsurfaces of the trihedral structure.

Retroreflectivity is a ratio of the amount of light returned from asurface versus the amount of light hitting that surface. Theretroreflective elements in retroreflective sheeting and materialsenhance retroreflectivity by utilizing the phenomenon of total internalreflection (TIR). TIR occurs when a propagated wave internally strikes amedium boundary at an angle of incidence relative to a lineperpendicular or normal to the boundary where the propagated wavestrikes the boundary that is larger than a particular critical anglewith respect to the normal to the boundary of that medium. The criticalangle is the angle of incidence above which the TIR occurs and is afunction of the relative difference between the indices of refraction ofthe two different materials that define the boundary.

TIR is particularly common as an optical phenomenon, where light wavesare involved, but it occurs with many types of waves, such aselectromagnetic waves in general or sound waves. When a wave reaches aboundary between different materials with different refractive indices,part of the wave will be partially refracted at the boundary surface andpart of the wave will be partially reflected. However, if the angle ofincidence is greater than the critical angle—the angle of incidence atwhich light is refracted such that it travels along the boundary—thenthe wave will not cross the boundary but will instead be totallyreflected back internally within that medium. This can only occur whenthe wave in a medium with a higher refractive index (n₁) reaches aboundary with a medium of lower refractive index (n₂).

Light beams or waves entering the front surface of a retroreflectivesheeting or material are measured according to an entrance angle that,like an angle of incidence, is determined relative to a normal of thesurface where the beam or wave enters the surface. Depending upon theentrance angle and the differences in the indices of refraction, thelight beams may experience TIR internal to the medium of theretroreflective sheeting or material and are then completely reflectedinternally within the medium and back out in the direction from whichthe light beams came. Ideally, such retroreflective sheeting or materialshould be able to retroreflect light beams entering the front surfacenot only at low entrance angles that are near zero (i.e. in a directionnear normal to the sheeting), but also at high entrance angles. Becausethe ability to internally reflect light at high entrance angles isdependent on the difference between the indices of refraction of thematerial forming the retroreflective elements and the material thatinterfaces with the back surface, many versions of retroreflectivesheeting provide an air space behind the retroreflective elements inorder to maximize this difference. However, even when such an air spaceis used, light entering the retroreflective elements beyond a certaincritical angle will leak out as partially refracted light, therebyreducing the retroreflectivity of the sheeting. Air spaces behind thereflective base material can also cause problems with durability andwith the infusion of foreign, life-reducing materials.

To overcome these shortcomings, retroreflective sheeting has beendeveloped that employs, in lieu of air spaces, a solid backing layerhaving an index of refraction that is lower than the index of refractionof the material used to form the retroreflective elements. While suchsheeting is structurally sounder and stronger than comparable sheetingemploying air spaces behind the retroreflective elements, the ability ofsuch sheeting to provide TIR for a broad range of entrance angles issignificantly less than that of air-backed articles because thedifference in the index of refraction between the material forming theretroreflective elements and the material forming the solid backinglayer is less. For example, if the retroreflective elements are cubecorners formed from polycarbonate having an index of refraction n=1.59,and the solid backing material is cryolite having an index of refractionof n=1.32, the difference between the indices of refraction is1.59−1.32=0.27. By contrast, when the backing layer is formed from airhaving an index of refraction n=1.00, the difference between the indicesof refraction is 1.59−1.00=0.59 which is more than twice as much as0.27.

To increase the critical angle for TIR, materials having an index ofrefraction lower than cryolite have been used in such retroreflectors.For example, a thin optical film formed from particulate metal oxidesuch as silicon dioxide or alumina mixed with a binder has been appliedas a backing layer to retroreflective sheeting. The resulting backinglayer is characterized by nanoporosity and can have an index ofrefraction as low as 1.10.

Another approach to increase the entrance angle at which aretroreflector exhibits some degree of retroreflectivity is to apply areflective metallic layer such as vacuum-deposited aluminum to the backsurface. In such a structure, when light enters the cube corners, forexample, it exhibits specular reflection off of the metallic layer whenit reaches the faces of the cube corners, and is retroreflected backtoward its source, even when entering at angles beyond the criticalangle for TIR in an air-backed structure. In addition to increasing theentrance angle at which the retroreflector exhibits some degree ofretroreflectivity, metallization provides a seal over the back surfaceof the retroreflective elements that prevents TIR-destroying dirt andmoisture from lodging on the back surfaces which would in turn degradeor destroy the ability of the retroreflective elements to provide TIR.

Unfortunately, metallization has the disadvantage of reducing theoverall retroreflectance of the article. Unlike TIR, for whichreflectance is 100%, aluminum has a reflectance of only about 85%.Consequently, the intensity of a retroreflected ray of light that isreflected off of three aluminized faces is reduced to about (85%)³ orroughly 61% of its corresponding TIR intensity.

Illustrative examples of cube corner type retroreflectors are disclosedin U.S. Pat. No. 3,541,606 (Heenan), U.S. Pat. No. 3,712,706 (Stamm),U.S. Pat. No. 3,810,804 (Rowland), U.S. Pat. No. 4,025,159 (McGrath),U.S. Pat. No. 4,202,600 (Burke), U.S. Pat. No. 4,243,618 (Van Arnam),U.S. Pat. No. 4,349,598 (White), U.S. Pat. No. 4,576,850 (Martens), U.S.Pat. No. 4,588,258 (Hoopman), U.S. Pat. No. 4,775,219 (Appeldorn), U.S.Pat. No. 4,895,428 (Nelson), U.S. Pat. No. 5,450,235 (Smith), U.S. Pat.No. 5,691,846 (Benson), U.S. Pat. No. 6,470,610 (Northey), U.S. Pat. No.6,540,367 (Benson), U.S. Pat. No. 7,156,527 (Smith), and U.S. Pat. No.9,703,023 (Smith).

Various attempts have been made to produce retroreflectors that enhanceperformance and/or improve on the entrance angles at which TIR occurs.U.S. Pat. No. 6,172,810 (Fleming) discloses wrapping the cube corners ofa reflective layer within multiple layers of polymer coating materialhaving different indices of refraction. U.S. Pat. No. 6,883,921 (Mimura)discloses specific packing and angular arrangements of cube cornerswithin different zones of a reflective layer to improve entrance angleperformance. U.S. Pat. No. 7,784,952 (Yukawa) discloses a sheetingmaterial with improved entrance angle performance produced with embeddedglass beads used as a focusing layer for a metal reflective layer on theback side of the focusing layer. U.S. Pat. No. 8,651,720 (Sherman) addsa viscoelastic light guide to some embodiments of retroreflectivesheeting. U.S. Pat. No. 9,575,225 (Kim) discloses a step retroreflectorfor improved entrance angle performance by using a main cube corner withsub-reflective corners on a shared surface to increase performance inthe axis orthogonal to the step retroreflector. U.S. Pat. No. 9,651,721(Chapman) discloses increased entrance angle performance by increasingthe difference between the indices of refraction a retroreflective layerand by lowering the index of refraction and providing nanopore structurein a backing material layer. U.S. Pat. No. 9,910,194 (Benton Free)discloses both optically active and inactive regions of theretroreflective sheeting. U.S. Pat. No. 9,971,074 (Chatterjee) disclosesthe addition of an amorphous polymeric layer between the body layer andthe cube corner elements to increase brightness.

Most retroreflective articles used in connection with transportationapplications have been optimized for nighttime detection in the visiblespectrum, roughly 400-700 nanometers. With the advent of ADAS (AdvancedDriver Assist Systems), ACC (Adaptive Cruise Control), LDW (LaneDeparture Warning) Systems, LKS (Lane Keep Systems), and CAVs (Connectedand Automated Vehicles), many automotive deployments are resorting toNIR (Near Infrared) active sensors to perform object sensing anddetecting.

Various attempts have been made to enhance and/or provide selectiveretroreflective articles in different spectral ranges other than thevisible spectrum. U.S. Pat. No. 8,496,339 (Nakajima) discloses anoptical structure layer and a wavelength selective reflective layer tocontrol the range of wavelength subject to retroreflection. U.S. Pat.No. 8,783,879 (Smith) teaches altering the performance characteristicsof a cube corner design by introducing roughness into cube corner faces.U.S. Pat. No. 9,746,591 (Lu) discloses a multilayer retroreflective filmthat improves structural integrity by using a strengthening layer andbuffering sections between retroreflective elements in theretroreflective layer. U.S. Pat. No. 9,964,676 (Nagahama) discloses awavelength selective retroreflective material that includes aconcavo-convex surface with first and second structural elements withdifferent angles for aspects of the cube corners in the retroreflectivelayer.

Prior art pavement marking materials, and even road signage, can exhibitreduced performance in wet conditions due to varying optical paths forwet and dry conditions. Techniques used to increase performance forwet/dry pavement marking articles, for example, include approaches likeadding glass or ceramic beads of different diameters to the articlesurface to account for varying optical paths for wet and dry conditions.This construction increases the cost of the article and reduces thedurability.

In view of the increased requirements for retroreflective articlesdesigned for use with autonomous vehicle machine visions systems, thereis a need for new approaches to the design, construction and use ofretroreflective articles that can improve both daytime and nighttimeperformance, can be applicable to both visible and NIR spectrums, and/orcan provide more consistent performance in different environmentalconditions.

SUMMARY OF THE INVENTION

In embodiments, ultrawide angle reflective articles and materials areenabled that effectively increase the entrance angle range for which thearticles exhibit total internal reflection (TIR) thereby increasing thenet retroreflectivity of these articles and materials. Articles andmaterials that exhibit TIR over ultrawide angle ranges produce a netincrease in retroreflectivity versus articles or materials that rely onspecular or diffuse reflection for repelling or directingelectromagnetic radiation. Articles and materials with ultrawide angleranges of TIR also exhibit improved reflective efficiency across abroader spectrum of electromagnetic radiation and in differentenvironmental conditions.

In various embodiments, ultrawide angle reflective articles or materialshave multiple retroreflective layers. A base retroreflective layer isprovided for reflecting electromagnetic radiation at low entrance anglesand can utilize retroreflective elements that rely on conventional TIRor other retroreflection techniques. A mezzanine retroreflective layeris provided with tilted cube corner elements that enable TIR forreflecting electromagnetic radiation at higher entrance angles but arebi-directionally transmissive for electromagnetic radiation at lowerentrance angles. Additional optical and backing layers can be providedin addition to the base and mezzanine retroreflective layers. In someembodiments, the multiple retroreflective layers are combined in anintegrated article or material. In other embodiments, the mezzanineretroreflective layer is provided as an overlay to be applied to anexisting retroreflective article or materials that then serves as thebase layer of the ultrawide angle reflective article or material.

In embodiments, reflective traffic sign sheeting is enabled withimproved entrance angle performance based on extending the ultrawiderange of angles that exhibit TIR. Medium materials for sign sheetingexhibit properties that include high or total transparency to thewavelength of radiation utilized with the article and a sufficientlyhigh index of refraction to support TIR at ultrawide entrance angleswith ranges greater than, for example, in some embodiments +/−35 degreesfrom normal and in other embodiments +/−60 degrees from normal. Basematerials for sign sheeting exhibit a sufficiently low index ofrefraction to support TIR at the desired entrance angles. Thecombination of the tilted geometric structure of the TIR portion of themezzanine layer and the normal geometric structure of the base layerprovides increased TIR ultrawide angle performance over traditional andprior art geometries.

In embodiments, ultrawide angle reflective sheeting is enabled thatexhibits sufficient flexibility to allow the production, shipping andstorage of materials in rolled form. Flexible sheeting can also be usedfor adherence to non-flat surfaces. In embodiments, flexible sheeting isenabled with medium materials that exhibit the desired flexibility ofthe manufactured article.

In embodiments, an overlay for existing sign sheeting material isenabled with improved entrance angle performance based on the ultrawiderange of entrance angles that exhibit TIR. In embodiments, a mezzaninelayer overlay exhibits flexibility allowing it to be manufactured,packed, and shipped in roll form.

In embodiments, reflective roadway pavement marking material is enabledwith improved entrance angle performance due to increasing the ultrawiderange of entrance angles that exhibit TIR. In embodiments, reflectivepavement marking materials are enabled that, upon installation on aroadway, have a substantially flat upper surface that exhibits TIR forultrawide entrance angles. The ultrawide angle TIR performance range ofembodiments is essentially similar for both dry and wet roadwayconditions.

In embodiments, an ultrawide angle reflective pavement marking isenabled that exhibits sufficient flexibility to allow the production,shipping, and storage of materials in rolled form. A flexible pavementmarking is enabled for adherence to a non-flat surface. In embodiments,a flexible pavement marking material is enabled with a medium materialthat exhibits the desired flexibility of the manufactured article.

In embodiments, a fiducial traffic sign design and layout is enabledthat, when broadly deployed and integrated into a vehicle safety system,can facilitate reduced traffic accidents, fewer vehicle operatorfatalities, and improved optical interaction between a roadwayinfrastructure and a human vehicle operator. In embodiments, a fiducialtraffic sign design and layout is enabled that, when broadly deployedand integrated into an autonomous or semi-autonomous vehicle safetysystem, can facilitate reduced traffic accidents and improvedelectromagnetic wave interaction between a roadway infrastructure andvehicle-based machine vision sensors.

With the advent of vehicle-based machine vision sensors that outperformthe human vision system, vehicle safety system functionality willinclude the presentation of sensed roadway elements to a human vehicleoperator. In embodiments, a Heads-up Display (HUD) is enabled thatpresents an image of a vertically-oriented fiducial sign detected alonga roadway. The location, size, and orientation of the fiducial signwould appear on the HUD appreciably similar to the vehicle operator asthe non-blocked or non-attenuated optical view an operator wouldexperience through a windshield in a vehicle traversing a roadway.Potential scenarios whereby the presentation of a fiducial sign on a HUDwould increase vehicle safety could include, but not be limited to aheavy rain environment, atmospheric conditions that includeeyesight-limiting or eyesight-blocking fog or dust, and vehicleoperators with reduced or compromised eyesight.

Horizontally-oriented roadway elements like pavement markers and roadedges can experience reduced optical detection and complete opticalblockage to vehicle-based optical sensor systems. In embodiments, anelectronic map with precisely-positioned roadway elements that includefiducial signs is used to present the optically-blocked roadway elementson a HUD in a proper location, size, and orientation so a human vehicleoperator can utilize the displayed and projected roadway elements toaccurately and safely operate a vehicle.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a plan view of a prior art cube cornerretroreflective sheeting.

FIG. 2 illustrates a cross-sectional view of the prior art sheeting ofFIG. 1.

FIG. 3 illustrates paths of light travel for TIR reflected rays for theprior art sheeting of FIG. 2.

FIG. 4 illustrates paths of light travel for mixed TIR and specularreflected rays for the prior art sheeting of FIG. 2.

FIG. 5 illustrates entrance angle performance for a cube corner designfor the prior art sheeting of FIG. 2.

FIG. 6 illustrates sign sheeting performance of a prior art cube cornerretroreflective sheeting at various entrance angles.

FIG. 7 illustrates the retroreflectivity response for a prior art cubecorner article.

FIG. 8 illustrates a cross-sectional view for a reflective article inaccordance with an embodiment of the present invention having a baseretroreflective layer and a mezzanine retroreflective layer.

FIG. 9A illustrates a plan view for tilted apex axis cube cornerretroreflective features for an embodiment of the mezzanine reflectivelayer as shown in FIG. 8.

FIG. 9B illustrates a more detailed plan view of a single tilted apexaxis cube corner retroreflective feature for FIG. 9A.

FIG. 9C illustrates a first cross-sectional view of a single tilted apexaxis cube corner retroreflective feature for FIG. 9B.

FIG. 9D illustrates a second cross-sectional view of a single tiltedapex axis cube corner retroreflective feature for FIG. 9B.

FIG. 10 illustrates a cross-sectional view of reflective sheeting inaccordance with an embodiment of the present invention with a normalapex axis cube corner base layer and a tilted apex axis cube cornermezzanine layer.

FIG. 11 illustrates the mezzanine layer retroreflectivity response forthe sheeting of FIG. 10.

FIG. 12 illustrates the combined base layer and mezzanine layerretroreflectivity response for the sheeting of FIG. 10.

FIG. 13 illustrates a sign construction with a backing material, asheeting material, and a mezzanine layer overlay in accordance with anembodiment of the present invention.

FIG. 14 illustrates improved entrance angle performance for foursheeting materials with mezzanine layer overlays in accordance withembodiments of the present invention.

FIG. 15 illustrates prior art definition of entrance angle for pavementmarkings.

FIG. 16 illustrates a sign or pavement marking embodiment with a tiltedapex axis cube corner construction.

FIG. 17 illustrates pavement marking entrance angle performance for aTIR article for the embodiment in FIG. 16.

FIG. 18 illustrates the pavement marking retroreflectivity response forthe embodiment in FIG. 16.

FIG. 19 illustrates wet article pavement marking retroreflectivityresponse.

FIG. 20 illustrates an embodiment of a proposed traffic sign design forsafety systems and machine vision systems.

FIG. 21 illustrates a positioning of the proposed traffic sign of FIG.20 along a roadway.

FIG. 22 illustrates a roadway with horizontal roadway elements obscuredby snow.

FIG. 23 illustrates a heads-up display that projects obscured roadwayelements.

DETAILED DESCRIPTION OF THE EMBODIMENTS

FIGS. 1 and 2 illustrate a portion of a typical replicated cube cornerretroreflective sheet 10 known in the prior art. Referring to both FIGS.1 and 2, reference 12 generally designates one of the minute cube cornerelements of formations prism features disposed in an array on one sideof sheeting 10. Each retroreflective element 12 has the shape of atrihedral prism with three exposed planar faces, substantiallyperpendicular to one another, and an apex axis defined by a lineintersecting the apex of the trihedral prism that is equidistant to eachof the planar faces. The angle between the faces of the trihedral prismis the same for each cube corner element in the array and will be about90 degrees.

As is illustrated in FIG. 2, cube corner elements 12 in sheet 10 can beall of the same dimensions and aligned in an array or pattern of rowsand columns, the bases being in the same plane, and adjacent elementsbeing contiguous at the edges of their bases such that there are nomargins or flats between adjacent elements or spaced apart as desired.If desired, different elements in the array may have varying dimensionsand orientations.

Body portion 16 is preferably integral with cube corner optical elements12, constituting what is referred to as a land that defines a frontsurface 18 into which electromagnetic radiation enters. The dimensionsof the land portion of the sheeting relative to the individual cubecorner optical elements will vary depending on the material of themedium of the sheeting, the method chosen for manufacture and,ultimately, the end purpose of the sheeting.

It is helpful to note that the trihedral prism elements 12 incross-sectional FIG. 2 are shown as effectively being upside-down from aconventional pyramid in that the apex 13 is below the base 14 which isoperably connected to the body portion 16. The triangular structure ofthe trihedral prism element 12 that provides the total internalreflection (TIR) phenomenon is the inverted shaded shape shown in thiscross-section as the figure portion of a figure-ground representation,and not the corresponding unshaded upright triangular shape that iseffectively the ground portion in this representation.

Cube corner elements of the prior art produce retroreflection due toTIR. Faces of cube corner elements will produce TIR when rays, beams, orelectromagnetic waves strike the internal boundaries of the mediumforming the retroreflective elements at an angle of incidence greaterthan the critical angle. The critical angle is measured from the normalvector to each boundary. For retroreflective articles and materials, itis common to refer to the angle of the incoming rays, beams orelectromagnetic waves that strike the front surface of the material orarticle as being the entrance angle, whereas the angles of the ray, beamor wave as it propagates internally within the medium and encounters oneor more additional boundaries, such as the face of a cube corner, arereferred to as the incidence angles or angles of incidence.

FIG. 3 shows two examples of incoming light rays 20, 34 that experiencetotal internal reflection (TIR) at the surfaces of the cube cornerelements of prior art retroreflective articles. The first ray 20 entersthe front surface of the reflective material essentially parallel to thenormal vector of the reflective material surface and travels through amedium 22 with a higher index of refraction than the backing material 24at a point 26 on the boundary of the backing material. Because theincident angle is greater than the critical angle, TIR projects thereflected ray 28 toward a second face of the cube corner element. Uponmeeting the second face of the cube corner element, the ray 28experiences TIR at point 30 and is completely reflected along ray 32.Rays 20 and 32 are essentially parallel and in opposite directions, thusproviding TIR retroreflectivity.

In contrast to light ray 20 which was perpendicular to the frontsurface, light ray 34 is non-parallel to the normal vector for the pointat which light ray 34 intersects the front surface of the reflectivematerial. Because light ray 34 encounters the cube corner boundary atpoint 36 at an incidence angle greater than the critical angle, lightray 34 also experiences TIR. The reflected ray 38 encounters the secondcube corner face at point 40 at an incidence angle greater than thecritical angle, also experiencing TIR. Rays 34 and 42 are essentiallyparallel and in opposite directions, thus providing TIRretroreflectivity.

FIG. 4 shows examples of rays 50, 62, 74 that experience retroreflectiveloss due to incident angles that are less than the critical angle andtherefore do not conform to the geometry of TIR in prior artretroreflective articles.

In a first example, ray 50 strikes the front surface of the medium at anentrance angle that is less than the critical angle and so enters themedium. After ray 50 enters the medium it encounters the first cubecorner face at point 52 at an incidence angle greater than the criticalangle and experiences complete internal reflection off of the first cubecorner face. The reflected ray 54 encounters the subsequent cube cornerface at point 56 at an incidence angle that is less than the criticalangle. Unlike the interaction with the first cube corner face, theinternal interaction with the second cube corner face causes a portionof the reflected ray 54 to refract through the barrier along ray 58 anda portion of the reflected ray 54 to experience specular reflectionalong ray 60. As a result, even though there was complete reflectioncaused by the interaction with the first cube face, there is not TIRbecause the interaction with the second cube face did not result incomplete internal reflection.

As a second example in FIG. 4, incoming ray 62 strikes the front surfaceof the medium at an entrance angle that is less than the critical angleand so enters the medium. After ray 62 enters the medium it encountersthe cube corner face at point 64 at an incidence angle that is less thanthe critical angle. A portion of the incident ray 62 refracts throughthe barrier along ray 66 and a portion of the incident ray 62experiences specular reflection along ray 68. Reflected ray 68encounters the cube corner at point 70 and experiences complete internalreflection along ray 72 because the angle is greater than the criticalangle. The retroreflected ray 72 is parallel to and in the oppositedirection of the incident ray. Its intensity, however, is less than theintensity of a full TIR path because of the loss due to specularrefraction that occurred at point 64.

As a third example in FIG. 4, incident ray 74 strikes the front surfaceof the medium at an entrance angle that is less than the critical angleand so enters the medium. After ray 74 enters the medium it encounters acube corner surface at point 76 at an angle that is less than thecritical angle. A portion of the incident ray 74 refracts through thebarrier along ray 78 and a portion of the reflected ray 54 experiencesspecular reflection along ray 80. Because the reflected ray does notencounter a second surface of the cube corner, the direction of the ray80 as it exits the medium is non-parallel to the incident ray 74 andproduces little or no retroreflectivity.

TIR retroreflectivity for an article with a flat front surface and acube corner back surface will be defined by the indexes of refraction ofthe medium that contains the article (typically air), the index ofrefraction of the material used to produce the article, and the index ofrefraction of the material behind the cube corner elements (alsotypically air). FIG. 5 shows the geometry for TIR for a typical priorart retroreflective article. The critical angle at the cube cornersurface is referenced from the cube corner normal vector 92 and isdefined by Snell's law:

η₁*sin θ₁=η₂*sin θ₂   Eq. 1

where η₁ is the index of refraction of medium 1

-   -   θ₁ is the angle of the wave in medium 1    -   η₂ is the index of refraction of medium 2    -   θ₂ is the angle of the wave in medium 2

For a medium 104 made of a material having an index of refraction of 1.6and with a cube corner backing 106 interfacing with air having an indexof refraction 1.0, the critical angle at the cube corner surface equatesto 38.7 degrees from the cube corner normal vector 92. The angle 91between the cube corner normal 92 and the surface normal 90 is 45degrees, so the internal range of TIR angles 94, 96 within the medium isdefined as:

+/−(cube-corner-normal−critical angle)   Eq. 2

or +/−6.3 degrees.

Incoming waves will be refracted when entering the front surface 102 ofthe medium 104 if the entrance angles are less than the critical angle.Using Eq. 1 and the index of refraction of the medium 104 and air as themedium interfacing with the front surface 102, the range 95 of TIRangles 98, 100 entering the medium 104 from air is +/−10.1 degrees.

To summarize FIG. 5 and the TIR geometry of a typical prior art cubecorner-type of retroreflective article or material, a trihedral prismwith three exposed planar faces in which an apex axis of the prism isparallel to the surface normal 90 will produce TIR when light waves haveentrance angles relative to the surface normal 90 that are smaller thanthe range defined by ray 98 and ray 100.

FIG. 6 shows images 110, 112, 114, 116 collected from a sign panelutilizing conventional retroreflective materials at four differententrance angles. The panel contains various colors of sheeting types,with white sheeting in the leftmost column of the panel. Images werecollected with an 850 nm active camera, and the lower four rows ofsamples contain sheeting types that conform to TIR geometries producedwith vertically-aligned prism apexes in a conventional retroreflectivematerial. Sample 118 is ASTM Type IV white sheeting, sample 120 is ASTMType VIII white sheeting, sample 122 is ASTM Type IX white sheeting, andsample 124 is ASTM Type XI white sheeting. Image 110 was collected at a0-degree entrance angle and shows the baseline intensity levels. Image112 was collected at a 20-degree entrance angle and shows reducedintensity levels. Image 114 at a 40-degree entrance angle and image 116at a 60-degree entrance angle show dramatic reduction of intensitylevels at these higher entrance angles in conventional retroreflectivematerials.

FIG. 7 shows a graph 130 of reflected intensity value 132 versusentrance angle 134 for a retroreflective element of a conventionalretroreflective material having an apex axis that is parallel to thesurface normal. The narrow, central part of the curve 136 showsintensity values for the range 138 of smaller entrance angles thatproduce TIR retroreflectance. The intermediate entrance angle ranges140, 141 produce intensity curves 142, 143 that are a result of acombination of TIR retroreflectance and internal spectral reflectance.The outer entrance angle zones 134, 135 representing larger entranceangles produce intensity values 144, 145 that are a result ofdramatically lower levels of TIR and internal spectral reflectance.

For purposes of describing the various embodiments, the followingterminology and references may be used with respect to retroreflectivearticles or materials in accordance with one or more embodiments asdescribed.

“Surface” means an exterior boundary of an article or material. In someembodiments, a surface may interface with air or vacuum at leastpartially surrounding the article or material. In other embodiments, asurface may interface with another object, such as a lens or coating. Asurface may be comprised of one or more facets, and may be either rigidor flexible in form, smooth or rough in texture, and homogeneous orheterogeneous in composition.

“Front surface” means a surface of an article or material exposed toelectromagnetic waves, beams, or rays that strike the article ormaterial and may be reflected or refracted by the article or material.“Back surface” means a surface of an article or material generallyopposite from a front surface.

“Layer” means a region of an article or material having thicknessrelative to a front surface of the article or material. In someembodiments, a layer may be a region of a medium of generally uniformthickness presenting an area that is substantially parallel inorientation to an orientation of the front surface of the article ormaterial, and in some embodiments a layer may have varying thickness andpresent an area that is not of generally uniform thickness orsubstantially parallel in orientation to an orientation of the frontsurface of the article or material. In some embodiments, a layer may becoextensive with an area of the front surface of the article ormaterial, and in other embodiments, a layer may not be coextensive withan area of the front surface. In some embodiments, a layer may begenerally rigid and planar, and in other embodiments, a layer may begenerally flexible. In some embodiments, a layer may be a medium that ishomogenous in composition or construction, and in other embodiments, alayer may be of a medium that is non-homogenous and non-uniform incomposition or construction.

“Normal” describes a direction that intersects a surface or boundary atright angles.

“Entrance angle” is defined as the angle relative to normal of a ray,beam, or wave of electromagnetic radiation as it strikes the frontsurface.

“Boundary” is a change of medium defined by a face, facet, surface,and/or material having a different index of refraction.

“Incidence angle” or “angle of incidence” is defined as the anglerelative to normal of a ray, beam, or wave of electromagnetic radiationas it strikes a boundary within an article or material.

“Cube corner element” describes a TIR retroreflective element, such as atrihedral pyramid, having multiple faces of the pyramid oriented at 90degrees with respect to each other.

“Apex” means the tip of a cube corner pyramid as defined by theintersection of the edges of the faces of the pyramid other than theedges of the base of the pyramid.

“Apex axis” means a line intersecting the apex of a cube corner pyramidthat is equidistant from each face of the pyramid.

“Near-normal TIR range” means a range of entrance angles which produceTIR based only on a retroreflection by a single layer of retroreflectiveelements for a given type of medium and retroreflective elements.

“Net retroreflectivity” means a combined retroreflectivity produced byretroreflective elements arranged in more than a single layer of areflective article or material.

“Ultrawide angle” means a range of angles for which TIRretroreflectivity occurs as a result of net retroreflectivity that isgreater than a near-normal TIR range for a given type of medium andretroreflective elements. In various embodiments, ultrawide angle maymean +/−35 degrees, +/−40 degrees, +/−45 degrees, and +/−60 degrees.

“ASTM D4956” means the ASTM International (formerly the American Societyfor Testing and Materials) standard ASTM D4956-19, StandardSpecification for Retroreflective Sheeting for Traffic Control, ASTMInternational, West Conshohocken, Pa., 2019, www.astm.org. ASTM D4956defines minimum retroreflectivity performance requirements forcommonly-used ASTM sheeting types like I, II, III, IV, VII, VIII, IX, Xand XI. Retroreflectivity requirements are established based on theobserver's or sensor's observation angle and entrance angle, and minimumretroreflectivity levels are expressed in units of candelas*lux⁻¹*m⁻².For ultrawide angle performance versions of ASTM sheeting types thatmeet enhanced performance specifications for retroreflectivity at largerentrance angles, the units of measure for retroreflectivity can beexpressed in units other than candela or lux (which are used based onthe response of the human eye to light in the visible spectrum) suchthat the units are valid for light sources and sensors in the range of400-1000 nanometers that includes the near infrared spectrum.

“Transparent” means a degree of clarity of a material as measured by theability to transmit image-forming light through the material. Themeasure of light transmission expressed in terms of transparency ortransmissivity is a ratio of the light intensity measured with a sampleof the material present in the light beam versus with the sample of thematerial not present in the light beam. For various embodiments, amaterial is considered to be transparent if the transmissivity is atleast 95% for light at 550 nm as measured according to ASTMInternational standard ASTM D1746-17, Standard Test Method forTransparency of Plastic Sheeting, ASTM International, West Conshohocken,Pa., 2019, www.astm.org. For other embodiments with more transparency, amaterial is considered to be transparent if the transmissivity is atleast 97% for light at 550 nm as measured according to ASTM D1746. Foreven more transparency for other embodiments, a material is consideredto be transparent if the transmissivity is at least 99% for light at 550nm as measured according to ASTM D1746. Like retroreflectivity,standards for measuring transparent materials are measured in thevisible spectrum. Given that the ultrawide angle performance inembodiments includes light spectrums beyond the visible spectrum thatinclude near-infrared wavelengths of light, the measure of transparencyor transmissivity for visible light frequencies and for frequenciesbeyond those of the visible spectrum would be made consistent with thestandards for measuring transparency. For the present disclosure amaterial is considered a transparent sheet-type material in thewavelengths beyond 700 nm if the transmissivity as measured consistentwith ASTM D1746 for light at 850 nm is at least set forth in the atleast 90% of the transmissivity as measured for light at 550 nm, and thetransmissivity as measured consistent with ASTM D1746 for light at 1000nm is at least set forth in the at least 85% of the transmissivity asmeasured for light at 550 nm.

FIG. 8 illustrates an embodiment for a reflective article 150 inaccordance with various aspects of the present inventions that containsa mezzanine retroreflective layer 152 operably connected to a baseretroreflective layer 154.

The properties of the base retroreflective layer 154 of variousembodiments are similar to prior art retroreflective articles thatutilize TIR from cube corner elements 155, for example, utilizing amaterial or materials that result in TIR reflectance within anear-normal TIR range 158 of angles 164, 166 that is relative to asurface normal shown at 156.

There are various properties of the mezzanine retroreflective layer 152in various embodiments that may differ from the properties of aconventional base retroreflective layer 154. First, the mezzanineretroreflective layer 152 produces a substantially unmodified internalpath for incident and reflected rays having an entrance angle in therange 158 of angles for TIR reflectance 164, 166 such that the mezzanineretroreflective layer 152 propagates these rays with entrance anglewithin the near-normal TIR range 158 to the base retroreflective layer154.

Second, the mezzanine retroreflective layer 152 produces TIR reflectancefor some, most, or all of rays that have entrance angles in the range ofangles 160, 162 that lie outside the near-normal TIR range 158 for thebase retroreflective layer 154. Third, the mezzanine retroreflectivelayer 152 produces an increase of entrance angles which are outside ofthe near-normal TIR range 158 for rays entering the front surface fromall directions, not just a particular dimensional direction.

FIG. 9A shows geometry of a cube corner architecture of embodimentswherein the apex axis of the faces of the trihedral prism used as theretroreflective element in the mezzanine layer is tilted relative tonormal of a front surface of the article or material. As shown, forexample, in FIG. 9B, each repeating structure of a cube corner featurein this embodiment consists of 18 faces organized as six groups of threecube corner faces 174, with each of the faces 174 of the cube cornergroups aligned generally 90 degrees from each other. The apex angle 184relative to a vector directly opposite the normal vector is determinedby the high point 170 of the cube corner structure and the low points172 of the cube corner structure. The cube corner geometry of the highpoint 170, low points 172 and the refractive indexes of the interfacingmaterials will determine the TIR incident angles at the surface ofretroreflective articles in accordance with these embodiments. The apexangle 184 as indicated along an apex axis 185 that is tilted relative toa vector directly opposite a normal vector entering the front surfaceindicates the relative tilt for the set of faces intersecting at thatapex of the trihedral cube corner for the base retroreflective layer.Cross-sectional representations of different aspects of the cube cornerstructure are shown in FIG. 9C and FIG. 9D. FIG. 9C shows what can becharacterized as a double bottom W shape indicating the angles of thefaces at the cross-sectional line taken at the bottom of FIG. 9B. FIG.9D shows what can be characterized as a single bottom W shape (shownrotated 90 degrees) and indicating the angles of the faces at thecross-sectional line taken at the right side of FIG. 9B.

FIG. 10 illustrates a two-layer article 180 produced from a singlearticle material with a structured embedded air mezzanine layer 182 anda structured base layer 186. The mezzanine layer 182 is configured as atrihedral prism with three planes, substantially perpendicular to oneanother, with the apex angle 184 of the prism having a tilted apex axisorientation as described in FIG. 9. The base layer 186 is configured asa trihedral prism with three planes, substantially perpendicular to oneanother, with the apex axis of the prism 198 in a non-tilted orientationand parallel to the surface normal of the article or material. In theembodiment shown, the angle between the faces 183 at the mezzanine layer182 and the faces 185 at the base layer 186 are roughly the same foreach cube corner element in each array, and in this embodiment are shownat about 90 degrees. In the cross-sectional view of this embodiment asshown in FIG. 10, the mezzanine layer 182 is depicted as a series ofgenerally W-shaped figures and the base layer 186 is depicted as aseries of generally V-shaped figures. Alternatively, constructions ofthe mezzanine retroreflective layer 182 in other embodiments may utilizea material other than air that has a low index of refraction sufficientfor TIR for the higher entrance angle rays to be retroreflected by themezzanine layer 182.

Ray 188 enters the article 180 at an angle that is sufficiently small(near normal) and will thus be within the near-normal TIR range for thecube corner base layer 186. Upon interaction with the near-horizontalface of the prism of mezzanine layer 182 the path of the ray 188 isessential unmodified as it passes through the embedded air gapassociated with the mezzanine layer 182. The light experiences TIR atthe faces of the base layer 186 cube corner structure 174 and isdirected back through the face 189 of the prism of mezzanine layer 182.The exiting ray is refracted at the article surface and produces a TIRray 190 that is essentially parallel to and in the opposite direction ofthe ray 188.

Ray 192 enters the medium at an angle that is beyond the near-normal TIRrange and is refracted at the surface of medium 180. The refracted ray194 encounters a near-horizontal face 195 of the prism in the mezzanine182 layer at an angle that is greater than critical angle, thusexperiencing TIR. The reflected ray encounters a face 197 of themezzanine 182 layer at an angle that is greater than the critical angleand also experiences TIR. The resulting ray 196 is refracted at thearticle 180 surface and is projected in a direction that is essentiallyparallel to and in the opposite direction of the ray 192.

The width of the gaps 199 of air or other material that form the facesof the trihedral prisms of the mezzanine layer 182 can be as small asone micron. In various embodiments, the width of the gap 199 should besufficiently large to produce TIR at the surface of the article 180 forultrawide angle rays. A completely connected trihedral prism structurecould, in practice, result in structural integrity issues of the articlewhen the prism material is air. In practice, and to increasemanufacturability and structural integrity, in various embodiments theintersection points of the trihedral prisms of the mezzanine layer 182can be filled with the article material without appreciable loss in TIRperformance. In other embodiments, face connection vias can be providedbetween the material faces of the gap 199 to further improve structuralintegrity.

FIG. 11 illustrates the response of the mezzanine layer and the sidelobes produced by an embodiment of a tilted apex axis cube cornergeometry. For FIG. 11, the cube corner parameters are:

η₀−index of refraction of air at article surface=1.0

η₁−index of refraction of article medium=1.6

η₂−index of refraction of mezzanine air gap=1.0

η₃−index of refraction of base layer air gap=1.0

base layer cube corner apex angle=180°

mezzanine layer cube corner apex angle=162°

Utilizing Eq. 1 and the indices of refraction (η₁ and η₂) the criticalangle for the mezzanine faces equates to 38.7°. In embodiments, therelatively lower indices of refraction of the body layer and/or themezzanine layer are relatively lower. In some embodiments, the indicesof refraction are less than 1.7. In other embodiments, the indices ofrefraction are less than 1.5. The equations for the minimum and maximumangles in the medium for the side lobes for TIR reflectivity for thevarious tilted apex axis are:

TIR-negative-lobe-min=(θ_(apex)−180)−(45−θ_(crit))   Eq. 3

TIR-negative-lobe-max=(θ_(apex)−180)+(45−θ_(crit))   Eq. 4

TIR-positive-lobe-min=−(θ_(apex)−180)−(45−θ_(crit))   Eq. 5

TIR-positive-lobe-max=−(θ_(apex)−180)+(45−θ_(crit))   Eq. 6

Where θ_(apex) is the angle of the apex of the cube corner elements

-   -   θ_(crit) is the critical angle relative to the normal of the        cube corner faces

Utilizing a cube corner apex angle of 162 degrees equates to side lobeswith TIR ranges of −24.3 to −11.7 degrees and 11.7 degrees to 24.3degrees. Because these angular ranges are within the article medium,they must be converted to in-air angles by utilizing Eq. 1 with theindexes of refraction for air and the medium. Eq. 1 determines thein-air TIR angular limits as −61.5 to −34.4 degrees and 34.4 to 61.5degrees. The table below shows some side lobe behavior based on varyingsome geometry and material parameters. For the table headings, η₀ is theindex of refraction of the air layer above the medium, η₁ is the indexof refraction of the medium, η₂ is the index of refraction of thematerial that forms the gap at the mezzanine layer, and η₃ is the indexof refraction of the material that forms the gap at the base layer. TheMezz layer apex angle is the tilt of the particular cube corner elementconfiguration as measured relative to a vector directly opposite anormal vector entering the front surface.

Base layer Base layer Mezz layer Mezz layer Mezz layer Mezz layer η₀ η₁η₂ η₃ crit. Angle TIR max apex angle crit. Angle TIR min TIR max 1 1.6 11 38.7 10.1 162 38.7 34.4 61.5 1 1.6 1 1 38.7 10.1 164 38.7 38.1 67.7 11.6 1 1 38.7 10.1 167.36 38.7 44.6 89.2 1 1.7 1 1.1 40.3 8 158 36 24.364.2 1 1.7 1 1.1 40.3 8 160 36 28 71.8 1 1.7 1 1.1 40.3 8 162.06 36 31.989.2 1 1.8 1.1 1.2 41.8 5.7 156 37.7 25.2 58.7 1 1.8 1.1 1.2 41.8 5.7158 37.7 29.1 65.4 1 1.8 1.1 1.2 41.8 5.7 161.41 37.7 36 88.8

The article response 210 for the mezzanine layer in FIG. 11 shows theTIR range for negative angles 200, the TIR range for positive angles202, and the three ranges 204, 206, 208 that exhibit combinations of netretroreflectivity due to TIR and specular reflection.

FIG. 12 shows the combined response 220 for the mezzanine layer and thebase layer for a combined article. The response 220 has a middle lobe221 that is due to TIR for the base layer cube corner geometry and hastwo side lobes 222, 223 that are due to TIR for the mezzanine layer cubecorner geometry.

FIG. 13 shows a traffic sign 225 construction utilizing standard signsheeting material 227 with an ultrawide-entrance-angle overlay 228. Thebacking 226 for the sign is made from a material like aluminum, to whicha standard sign sheeting 227 material is affixed. The base sign material227 is selected from products that include, but are not limited to,embedded glass beads or retroreflective cube corners. The overlay 228exhibits the properties of TIR over ultrawide entrance angle ranges dueto side-lobe geometry while passing through low-entrance-angle rays foroptical processing by the base sheeting 227 material.

FIG. 14 shows the effect of adding an ultrawide overlay that containstilted apex axis, cube corner structures to the face of existing signsheeting materials. Images 230, 231, 233, 233 show the effect of amodified sign panel at four different entrance angles. The panelcontains various colors of sheeting types, with white sheeting in theleftmost column of the panel. Sample 234 depicts ASTM Type IV whitesheeting with a tilted apex angle cube corner overlay as a mezzaninelayer, sample 235 depicts ASTM Type VIII white sheeting with a tiltedapex angle cube corner overlay as a mezzanine layer, sample 122 depictsASTM Type IX white sheeting with a tilted apex angle cube corner overlayas a mezzanine layer, and sample 124 depicts ASTM Type XI white sheetingwith a tilted apex angle cube corner overlay as a mezzanine layer. Image230 depicts a 0-degree entrance angle and shows the baseline intensitylevels. Image 231 depicts a 20-degree entrance angle and showsappreciably similar intensity levels to the baseline levels. Image 232at 40-degree entrance angle and image 233 at 60-degree entrance angleshow no appreciable reduction of intensity levels.

The ASTM D4956 minimum requirements for three commonly-used sheetingtypes are:

Observation Angle Entrance Angle R_(A) Type IV White 0.1°  −4° 500 0.1°+30° 240 Type VIII White 0.1°  −4° 1000 0.1° +30° 460 Type IX White 0.1° −4° 660 0.1° +30° 370

Candela is a measure of luminous intensity and lux is measure ofluminance. Both measures are based on the response of the human eye tolight. As a result, both measures do not have utility outside thevisible spectrum (400-700 nm). With the advent of NIR sensors forvehicle safety systems and autonomous vehicle navigation, newperformance measures are required for road-based markers. One measure ofretroreflectivity can utilize milliwatts (mW) for reflected intensityand watts per square meter (W/m²) for incident intensity. Restating theASTM D4956 requirements for Types IV, VIII and IX sheeting and using theconversion factors of 1 W/m²=683 lux at 555 nm and 1 candela=18.399 mW,the minimum performance table can be restated as follows, withretroreflectivity expressed in units of milliwatts per watt per metersquared, or mW*W⁻¹*m⁻²:

Observation Angle Entrance Angle R_(A) Type IV White 0.1°  −4° 13.5 0.1°+30° 6.5 Type VIII White 0.1°  −4° 26.9 0.1° +30° 12.4 Type IX White0.1°  −4° 17.8 0.1° +30° 10.0

In embodiments, ultrawide angle performance versions of ASTM sheetingtypes are enabled that meet enhanced performance specifications forretroreflectivity at larger entrance angles. In embodiments, the unitsof measure for retroreflectivity are expressed in units that are validfor light sources and sensors in the range of 400-1000 nanometers. Thetable below shows minimum proposed performance levels for ultrawideangle versions of three popular ASTM sheeting types:

Observation Angle Entrance Angle R_(A) Type IV-WA White 0.1°  −4° 21.10.1° +30° 9.7 0.1° +60° 7.3 Type VIII-WA White 0.1°  −4° 24.2 0.1° +30°19.4 0.1° +60° 14.5 Type IX-WA White 0.1°  −4° 16.0 0.1° +30° 12.8 0.1°+60° 9.6

Ultrawide angle versions of ASTM sheeting types I, II, III, VII, X, andXI are enabled in embodiments. Suggested minimum performancespecifications for each ultrawide-angle type will utilize a baseperformance level of something less than a base performance of a similarnon-ultra wide angle type of sheeting to account for the potential lossof reflection through the mezzanine retroreflective layer. Performancelevel of at least about 90% of the base performance level as thenon-ultrawide angle type for −4 degree entrance angles. Performancelevels for +30 degrees for ultrawide angle sheeting may be establishedat a base level of at least about 80% of the −4 degree retroreflectivitylevel. Performance levels for +60 degrees for ultrawide angle sheetingmay be established at a base level of at least about 60% of the −4degree retroreflectivity level. Other performance level percentages forultrawide angle retroreflective articles may be utilized and would be inaccordance with other embodiments.

FIG. 15 shows a prior art description of pavement marking 242 geometry.A sensor is shown as vehicle 246 whereby the headlamps function as thesensor illuminator. The entrance angle 244 is defined as the angleformed by the vector from the illuminator to a point on the pavementmarker 242 and the normal vector to the same point on the pavementmarking 240. In the United States, pavement markers are typicallyevaluated utilizing a 30-meter geometry, consisting of a measurementdistance 248 of 30 meters and an entrance angle 244 of 88.76 degrees.

FIG. 16 shows a cross section of a pavement marking embodiment thatutilizes embedded TIR structures for increased retroreflectivity atultrawide angles. The pavement marker 250 is produced from a material254 that contains a structured air gap 252 formed as a tilted apex axiscube corner construction forming a mezzanine retroreflective layer. Theangle of the apex axis is selected appropriately to produce a TIR anglezone that extends to +/−90 degrees from the marker 250 normal. Light ray257 at a near-horizontal direction encounters the surface and isrefracted toward the structured air gap 252. Upon experiencing TIR atthe three faces of the cube corner, the resulting retroreflected ray isrefracted at the surface and the refracted ray 258 is roughly parallelto and in the opposite direction of the ray 257. Ray 255 enters themedium 250 at an angle that is outside the near-normal TIR range for thearticle. Because the refracted ray encounters the air gap at an anglethat is not greater than the critical angle, the ray passes through theair gap to the lower layer of the marker 250 where it experiencesspecular reflection. The reflected ray 256 exits the medium 250 at anangle that is near-parallel to and generally in the opposite directionof the incident ray 255.

FIG. 17 illustrates the relationship between the tilted apex axis cubecorner construction 266 of a pavement marker 250 and the range of angles260 that produce TIR reflectivity. The smallest negative TIR angle 262is near surface normal and the largest negative TIR angle 264 is at anangle that is well above the incident ray of any vehicle-based sensor ona roadway. Utilizing an air gap constructed from a tilted apex axis cubecorner geometry will require an apex angle that is selected based on theindex of refraction of the material that comprises the medium 250.Utilizing Equations 1, 3 and 4, the following table displays apex anglesand various materials that yield near horizontal TIR angles for thepavement marker 250. For the table headings, the index of refraction ofthe air layer above the medium is 1.0, η₁ is the index of refraction ofthe medium, and η₂ is the index of refraction of the material that formsthe gap at the cube corner structure.

Apex Min Neg. Max. Neg. Min Neg. Max. Neg. η₁ η₂ Angle TIR Angle TIRAngle TIR Angle TIR Angle 1.5 1.0 173.62 −89.7 −60.4 60.4 89.7 1.6 1.0167.36 −89.2 −44.6 44.6 89.2 1.7 1.0 162.06 −89.2 −31.9 31.9 89.2

FIG. 18 illustrates the response 270 of the pavement marker and the sidelobes produced by the tilted apex axis cube corner geometry utilizing amedium index of refraction of 1.6 and an apex angle of 167.36 degrees.The negative TIR lobe angular range 272 extends from essentially −90degrees to −44.6 degrees, and the positive TIR lobe angular range 274extends from 44.6 degrees to near 90 degrees. The middle range 276 ofangles produce a lower response because incident rays in this range donot experience TIR in the marker medium.

Pavement marker manufacturers will utilize techniques and materials atthe surface of their products to establish good performance in both dryenvironments and on wet roadways. Manufacturers will typically includetwo types of materials with varying geometries to account for differentindexes of refraction between dry surface elements and water-coveredroad surface elements. FIG. 19 illustrates an embodiment with a pavementmarker 250 with a flat surface that includes a non-vertical apex cubecorner TIR embedded structure with a lower index of refraction than themarker 250 medium. A layer of water 280 rests upon the marker 250.

Utilizing a medium index of refraction of 1.6, a structured air gapindex of refraction of 1.0, and an apex angle of 167.36 degrees, themedium exhibits a minimum negative TIR angle 282 of −38.68 degrees and amaximum negative TIR angle of −26.04 degrees. Utilizing an index ofrefraction of 1.33 for water, Eq. 1 produces a minimum negative TIRangle 286 of −48.74 degrees in water 280 and a maximum negative TIRangle 288 of −31.88 degrees in water 280. Utilizing an index ofrefraction of 1.0 for air, Eq. 1 produces a minimum negative TIR angle292 of −89.21 degrees in air and a maximum negative TIR angle 294 of−44.62 degrees in air. As shown by the computations for a water-coveredpavement marker 250, the minimum and maximum TIR angles 292, 294 for thepavement marker 250 are not affected by surface water on a medium with aflat surface.

Ultrawide angle reflective sign sheeting based on TIR described inembodiments enables new capabilities in automotive safety applications.FIG. 20 displays a proposed new “fiducial” traffic sign 360 design andlayout. The sign is produced with a white, wide-angle TIR sheetingmaterial 362 with a structured, non-reflective overlay 364. Proposeddimensions for a U.S. version of the fiducial sign 360 are:

Reference Description Dimension (inches) 366 sign height 12 368 signbase to overlay top 10 370 sign base to overlay cutout top 8 372 signbase to overlay cutout bottom 4 374 sign base to overlay bottom 2 376sign width 12 378 sign edge to right overlay edge 10 380 sign edge toright overlay cutout 8 382 sign edge to left overlay cutout 4 384 signedge to start of overlay 2

FIG. 21 displays a use of a fiducial sign 360 along a roadway 362. Signsare placed on each side of the road 362 and are at sufficient density soat least two consecutive signs on a side of the road are simultaneouslyavailable within the field of view of a typical machine vision sensor onboard a vehicle traversing the roadway. The ultrawide angle TIR propertyof the sign sheeting type allows the vehicle to be closer to thenear-range signs and still exhibit high-intensity sensing. A wide-anglesensor viewing of the ultrawide angle retroreflective signs will, as aresult, enhance the spatial accuracy of roadway elements that arereferenced relative to the fiducial signs.

FIG. 22 illustrates the roadway with visible fiducial signs 360 and anon-visible roadway due to snow 364 cover. The vehicle sensor detects asufficient number of fiducial 360 signs, thus allowing the vehicleprocessing system to determine the relative location of necessaryroadway elements.

FIG. 23 illustrates a use for the relatively-positioned roadway elementscontained within the vehicle's high-definition map containing previouslymapped locations of each roadway element. The vehicle windshield 370acts as a heads-up display (HUD) whereby the vehicle positioning systemcan accurately display messages and information. In this view theroadway signs are viewed through the windshield or are obscured by anattenuating environment like snowfall. The vehicle sensor, however,maintains optical contact with the fiducial signs and displays them onthe HUD 370. Other important roadway elements a like pavement surface372, edge lines 374 and centerlines 376 are displayed in properorientation to a driver or communicated to an autonomous control systemthat can accurately and safely navigate the roadway based on the addedroadway elements after corresponding the sensed roadway elements withthe high-definition map.

Persons of ordinary skill in the relevant arts will recognize thatembodiments may comprise fewer features than illustrated in anyindividual embodiment described above. The embodiments described hereinare not meant to be an exhaustive presentation of the ways in which thevarious features of the embodiments may be combined. Accordingly, theembodiments are not mutually exclusive combinations of features; rather,embodiments can comprise a combination of different individual featuresselected from different individual embodiments, as understood by personsof ordinary skill in the art. Moreover, elements described with respectto one embodiment can be implemented in other embodiments even when notdescribed in such embodiments unless otherwise noted. Although adependent claim may refer in the claims to a specific combination withone or more other claims, other embodiments can also include acombination of the dependent claim with the subject matter of each otherdependent claim or a combination of one or more features with otherdependent or independent claims. Such combinations are proposed hereinunless it is stated that a specific combination is not intended.Furthermore, it is intended also to include features of a claim in anyother independent claim even if this claim is not directly madedependent to the independent claim.

Any incorporation by reference of documents above is limited such thatno subject matter is incorporated that is contrary to the explicitdisclosure herein. Any incorporation by reference of documents above isfurther limited such that no claims included in the documents areincorporated by reference herein. Any incorporation by reference ofdocuments above is yet further limited such that any definitionsprovided in the documents are not incorporated by reference hereinunless expressly included herein.

For purposes of interpreting the claims, it is expressly intended thatthe provisions of Section 112, sixth paragraph of 35 U.S.C. are not tobe invoked unless the specific terms “means for” or “step for” arerecited in a claim.

1. An ultrawide angle retroreflective sheeting comprising: a body layerpresenting a front surface; a base layer retroreflective material havingan array of cube corner elements each with an apex axis having anorientation generally parallel to a normal of the front surfaceproximate the cube corner element; and a mezzanine layer retroreflectivematerial between the body layer and the base layer and having an arrayof cube corner elements configured with at least some of the cube cornerelements having an apex axis having an orientation generally tiltedrelative to a normal of the front surface proximate the cube cornerelement such that the mezzanine layer is reflective for electromagneticradiation striking the front surface at higher entrance angles above acritical angle but is bi-directionally transmissive for electromagneticradiation striking the front surface at lower entrance angles below thecritical angle.
 2. The sheeting of claim 1, wherein the body layer istransparent to wavelengths from 400-1000 nanometers.
 3. The sheeting ofclaim 1, wherein the base material cube corner elements produce hightotal internal reflection (TIR) for entrance angles from −10 degrees to+10 degrees.
 4. The sheeting of claim 1, wherein the mezzanine materialis transparent to wavelengths from 400-1000 nanometers.
 5. The sheetingof claim 1, wherein the mezzanine material cube corner elements producehigh total internal reflection (TIR) for entrance angles from −60degrees to −15 degrees and 15 degrees to 60 degrees.
 6. The sheeting ofclaim 1, wherein the body layer and the mezzanine layer retroreflectivematerial have relatively lower indices of refraction of less than 1.7.7. A retroreflective sheeting overlay article comprising: a body layerpresenting a front surface; a backing layer having an adhesive surface;and an intermediate layer material of retroreflective material betweenthe body layer and the backing layer having a texturized array of cubecorner elements configured with at least some of the cube cornerelements having an apex axis having an orientation generally tiltedrelative to a normal of the front surface proximate the cube cornerelement such that the mezzanine layer is reflective for electromagneticradiation striking the front surface at higher entrance angles above acritical angle but is bi-directionally transmissive for electromagneticradiation striking the front surface at lower entrance angles below thecritical angle.
 8. The article of claim 7, wherein the intermediatelayer material is transparent to wavelengths from 400-1000 nanometers.9. The article of claim 7, wherein the intermediate layer material cubecorner elements produce high total internal reflection (TIR) forentrance angles from −60 degrees to −15 degrees and 15 degrees to 60degrees.
 10. The article of claim 7, wherein the body layer and theintermediate layer material have relatively lower indices of refractionof less than 1.7.
 11. A retroreflective sign article, comprising: abacking material; and an approved sign sheeting material applied to thebacking material; and an overlay material applied to the sign sheetingmaterial constructed with a layer of texturized cube corner elementsconfigured with at least some of the cube corner elements having an apexaxis having an orientation generally tilted relative to a normal of thefront surface proximate the cube corner element such that the mezzaninelayer is reflective for electromagnetic radiation striking the frontsurface at higher entrance angles above a critical angle but isbi-directionally transmissive for electromagnetic radiation striking thefront surface at lower entrance angles below the critical angle.
 12. Thearticle of claim 11, wherein the overlay material is transparent towavelengths from 400-1000 nanometers.
 13. The article of claim 11,wherein the overlay material cube corner elements produce high totalinternal reflection (TIR) for entrance angles from −60 degrees to −15degrees and 15 degrees to 60 degrees.
 14. The article of claim 11,wherein the approved sign sheeting material is selected from thestandard sheeting types as defined in ASTM D4956 consisting of the setof: Type I, Type II, Type III, Type IV, Type VIII, Type IX, Type X, andType XI.
 15. A retroreflective sheeting comprising: a body layer formedof a material transparent to wavelengths from 400-1000 nanometers withan index of refraction less than 1.7 that presents a front surface; anda base layer formed of a retroreflective material having an array ofcube corner elements that is operably adhered to the body layer oppositethe front surface.
 16. A machine vision system for a vehicle,compromising: an active camera configured to dynamically image roadwayelements in a field of view from the vehicle, the roadway elementshaving an ultrawide angle retroreflectance that provideretroreflectivity values of at least 60% of the ASTM D4956 minimum valuefor −4 degree-entrance-angle retroreflectivity level for entrance anglesfrom −60 degrees to +60 degrees from a normal to a surface of thetraffic sign, and a processing system operably coupled to the cameraconfigured to identify the signs based at least in part on a sheetingtype having the ultrawide entrance angle retroreflectivity.
 17. Thesystem of claim 16, wherein the retroreflectivity values of the signs ata 30 degree entrance angle are at least 80% of the ASTM D4956 minimumvalues for retroreflectivity at a −4 degree entrance angle.
 18. Thesystem of claim 16, wherein the retroreflectivity values of the signs ata 60 degree entrance angle are at least 60% of the ASTM D4956 minimumvalues for retroreflectivity at a −4 degree entrance angle.
 19. Thesystem of claim 16, further comprising a heads-up display configured toproject a sign image based on an output of the processing system. 20.The system of claim 16, wherein the processing system includes adatabase of a map of locations of roadway elements and the processingsystem is configured to correlate imaged roadway elements with locationsof the roadway elements in the database and project the locations ofcorresponding roadway elements on the heads-up display in a locationrelative to the identified signs.